Pre-Calculus
Direct Variation and Hooke's Law
Name:
Date:
Overview
Today we are going to look at a relationship between two quantities called direct variation. We'll be
using a virtual laboratory involving simulated springs. In the end we will determine what Hooke's law is
and how we can use this to find the weight of unknown quantities. We will then use this skill to look at
other direct variation situation to solve for unknown quantities.
Procedure and Questions
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Open the website http://phet.colorado.edu/
Click "Play with Sims" Button
Click "Math" from the menu on the left side of the webpage.
Click on the "Masses and Springs" Activity
Click the "Run Now" Button
Hang the known weights onto the springs and record how much the weight moves any of the
springs (the springs are all the same.)
Trial Number
Weight Mass(grams)
Displacement (centimeters)
1
2
3
7. Graph these recordings using an x, y scatter plot. Let x be the weight used and y be the
displacement of the spring.
8. What do you notice?
9. What are the characteristics of this graph and their physical interpretation. (i.e. are there any
intercepts? What do they mean?)
10. What is the equation that relates the weight used, x, to the displacement y?
11. Using this equation and/or graph, what are the masses of the unlabeled weights?
Post Lab Discussion
This relationship between mass and displacement is known as Hooke's Law. It is an example of Direct
Variation. All direct variation relationships may be modeled by the function y = kx. We would say y
varies directly with x.
What is the value of k in your experiment, include units of measurement? This is called the spring
constant.
Now, if a different spring had a displacement of 2 cm for a 100 gram weight and a displacement of 4 cm
for a 200 gram weight, what would be the spring constant?
Next determine the mass of a weight that would create a 7 cm displacement using the spring in the last
question.
If we solve for k in any direct variation equation we end up with y/x = k. We found that all weights vary
directly to displacement by the same constant using the same spring. So if a spring gives us two data
entries of (x1,y1) and (x2,y2) then y1/x1 = k and y2/x2 = k. As such y1/x1 = y2/x2. Use this proportion to find
out how much a 500 g weight will displace on a spring if we know that a 175g weight displaced 3 cm.